Is counting on your fingers good, bad, or both? What do you think? Peter (Classroom Professor) analyzes the mathematical thinking in two classrooms, (giving finger counting a thumbs down, and visualizing a thumbs up) and Caroline (Maths Insider) says don't count onyour fingers! (In a series debunking math myths, I said go ahead, but these posts got me thinking. Now I'd say it's a starting point, and let's think about how to move on.)

John (Math Hombre) has made a game where you multiply and divide by fractions to make the superheroes shrink and grow, Size the Day.

John Henry is the legend of a steel-driving man who competed against a steam engine. David (Delta Scape) shares this story with school children, and then they time each other doing multiplication worksheets with and without a calculator. "Students are asked to predict which method will take longer, gather data, and compare the results using box-plots." Sounds like a good way to help students decide when it makes sense to use a calculator.

Michelle (The Rookery) used Incredible Comparisons: The World in One Day(only available used) to help her students understand rates. I've visited Michelle's classroom, and it feels magical to me. Here's a quote from a post on playing class games, "A
child who has fallen on his knees to plead with another child to 'smile if you love me' does not feel inhibited when it's time to raise
his hand and take a guess at how to solve a math problem."

(from Christy's Game of Patterns)

Patterns & Logic

Making up your own games is super-engaging. Christy (Just Another Step...) and her son made up a game of patterns that they had great fun with.

Logic puzzles can be a great side door into the mansion of math. (Think about how Sudoku has swept the country.) The Island of Liars and Truthtellers is a classic setting for logic puzzles. Dan (mathrecreations) shares some background and 5 puzzles.

Dr. Techniko's game, How To Train Your Robot, sounds like a blast, suitable for very young kids, whose 'robots' are their parents.

(from britton.disted.camosun.bc.ca/jbsymteslk.htm)

Visual Math

(by Anna Weltman)

Becky (Wide Open Campus) shares photos from her son Z's Escheriffic day, along with a link to a tessellation maker and some thoughts on the magic.

In Not Just Shapes, Malke (The Map is Not...) continues her delightful series documenting her daughter's math discoveries. "As the structure of the universe continues to emerge in front of her
very own (and open) eyes, how much more fun will her world be to play
in, explore, put together, and then take apart again?"

Justin (Math Munch) shares Star Art with the readers of Math Munch (a weekly math links blog), along with some puzzle news. (Links to directions for making this beautiful blue star are in the comments.)

Rachel (Plus Magazine) wrote Shattering Crystal Symmetries. If I understand correctly, chemists used to think crystals were always organized in a repeating pattern; Dan Schectman analyzed the structure of a crystal that could not have a repeating pattern, and won the 2011 Nobel Prize for chemistry for this work, which is based on the mathematical work of Roger Penrose. Amazing! "Not only had mathematicians extensively studied symmetry, but, as
mathematicians are prone to do, they were also interested in how to
break it."

In Perspective in Math and Art, Annalisa (at Inside Higher Ed) writes about how learning to draw in perspective can be a bridge to learning math. "If you sketch a picture of the rails of the train track going into the
distance, and you know where the first two railroad ties go, where do
you put the next one?"

(from Fawn's area of a circle lesson)

Algebra, Geometry, &Trigonometry

Kids are never too young to do some algebraic thinking with the Function Machine or Guess My Rule game. Denise (Let's Play Math!) spells it out carefully, and John (Math Hombre) writes about using it with college students, "7 to 1 and then 1 to 7 drew an audible gasp."

Smruti (Maths Study Blog) shows a method for finding simple side lengths when you have one side of a right triangle. One side is not enough to establish just one possible triangle, but if you'd like to play with finding Pythagorean triples (3 whole numbers giving the lengths of sides of a right triangle, like 3-4-5), then this technique is intriguing. [His site has flashing ads and brought up a pop-up window. I believe it's safe, but can't be sure.]

Haggis (Knot Your Average Sheep) helped design some activities for an interactive evening at the museum (National Museum of Scotland), and included this: "Can you colour the lines [on the star above] with 3 colours so that at each star 3 different colours meet?"

RobertAbbott (inventor of the card game Eleusis) has shared some great online Logic mazes.

Here's a puzzle from Alexander (Cut the Knot): Given a sequence of numbers, pick any two, say A and B, randomly and replace the two with the result of A×B+A+B. Repeat the procedure until only one number remains. Try to predict the final result. You can play with it online. What's happening?

(from Rick's blog banner)

Notation and Language

Sometimes the notation makes a math topic harder than it needs to be. Take logarithms, for example. Where'd that word come from, anyway? Kate (f(t)) uses power2(8) = 3 to invite her students to figure out what the new function is. I used her idea, but changed it to P2(x); it worked great.

Rick (Exploring Binary) wanted a word for the portion of a binary number after the ... umm, "decimal" point. You know, the part that represents a fraction. He wants to know if 'bicimal' works for you.

Peter and Christian (The Aperiodical, a math links blog) found a CNN story on an advance that may change public transportation, based on linear algebra. If a bus will be running more often than every 10 minutes, passengers can wait less if there's not a schedule. Each bus stops at each end of the line the right amount of time to average its time between the bus in front and behind it. Bus bunching (where one bus ends up right behind another) has always been a big problem, and this solves it. Most of the mathematical paper is quite readable.

Denise (Let's Play Math!) says, "What better way could there be to do math than snuggled up on a couch
with your little one, or side by side at the sink while your
middle-school student helps you wash the dishes, or passing the time on a
car ride into town?" Mmm, tell me a math story, please.

If you want students to learn math through projects (Project-Based Learning has its own acronym of course, PBL), you need to come up with projects that fit your subject and your teaching style. Bryan (Doing Mathematics) brainstorms some enticing ones. Geoff (emergent math) makes a plea for more inquiry-based lessons (is that the same as project-based?) He has set up a google docs repository for each course from algebra to calculus, and lots of folks have contributed ideas. You can use theirs or add some more.

And now we've come to the end of the 51st Math Teachers at Play blog carnival. Here's one last parting thought... I once read that, among the Tsilagi (Cherokee), you become an adult at 51. (Perhaps that's a bad translation, and you become an elder at 51?) That idea really stuck with me, and when I turned 51 I thought often about how much I'd matured since I was 18. With a 10-year-old in my life, I'm still working hard at maturity... What's 51 mean to you?

The next Math Teachers at Play blog carnival will be hosted at Denise's Let Play Math! blog in the 2nd week of July. If you'd like to be a host of this monthly carnival, check here for open dates. Until then, take your time to savor all these goodies, and when you're done here, check out the 87th Carnival of Mathematics at Random Walks.

I had a name and blog name wrong. (I got two people with similar names mixed up.) I fixed it, so now if you go to Bryan's (Doing Mathematics) brainstorm of some enticing projects, you won't be confused.

About Me

Math Mama is Sue VanHattum, a community college math teacher interested in all levels of math learning, and the mama of a young son. I entered the blogging world as I began work on an anthology about learning math. Contact me at mathanthologyeditor on gmail etc.